In the limit as a pulse width (τ) for a given frequency (υ) goes to infinity, the frequency spread generated by the fft of the waveform goes to what? explain. if one wants to deliver radiation with a given frequency of very high precision to a sample, does the pulse need to be ‘short’ or ‘long’ ? explain. consider two arbitrary waveforms: one waveform is very sinusoidal in nature, the other is very “step-ish” and had non-smooth appearance. what can be said about the relative spread or distribution of sin/cos functions needed to reconstruct these waveforms?

When the velocity of an object is doubled, by what factor is its momentum changed? by what factor is its kinetic energy changed? a) the momentum is zero. b) the momentum is not zero. c) difficult to say.

Because light travels in a straight line and casts a shadow, isaac newton hypothesized that light is

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?